Yeah, for example I was looking at NSF funding for grad school research and while your application is based on a research proposal, your research doesn't actually have to be what you proposed.
Both true but there are limits. Grad students are still defined by what they've done previously so while there is a lot of choice, it's still within a particular field (i.e. limited to a subset of the whole 'PhD-space').
That's probably stating the obvious (but sometimes it's worth doing that).
Edit: The analogy does works but you might want to consider subjects as 'startup areas' e.g. consumer, enterprise, infrastructure, etc
